Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

被引:15
作者
Srivastava, Hari Mohan [1 ,2 ,3 ,4 ]
机构
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
[3] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan
[4] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy
关键词
linear and bilinear generating functions; orthogonal polynomials; Jacobi; Laguerre and Hermite polynomials; Bessel polynomials; higher transcendental functions; Lagrange's expansion theorem; Bailey's bilinear generating function; Hille-Hardy formula; Mehler's formula; operational techniques; Laplace and inverse Laplace transforms; Riemann-Liouville fractional derivative; hypergeometric functions; hypergeometric polynomials; ENERGY SPECTRAL FUNCTIONS; JACOBI-POLYNOMIALS; ASYMPTOTIC-EXPANSION; PROOF; EXTENSIONS; FORMULAS; REPRESENTATION;
D O I
10.3390/math10203730
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions and hypergeometric polynomials in one, two and more variables. Many of the results as well as the methods and techniques used for their derivations, which are presented here, are intended to provide incentive and motivation for further research on the subject investigated in this article.
引用
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页数:23
相关论文
共 153 条
[1]  
ABRAMOWITZ M., 1972, Applied Mathematics Series, V55
[2]   ON SOME NEW TYPE OF GENERATING FUNCTIONS OF GENERALIZED POISSON-CHARLIER POLYNOMIALS [J].
Ahmed, Shakeel ;
Khan, Mumtaz Ahmad .
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 37 (01) :293-301
[3]  
Andrews G., 1999, SPECIAL FUNCTIONS EN, V71
[4]  
Andrews L.C., 1984, Special Functions for Engineers and Applied Mathematicians
[5]  
[Anonymous], 1956, AM MATH MON, DOI DOI 10.1080/00029890.1956.11988880
[6]  
Aomoto K, 2011, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-4-431-53938-4_1
[7]  
Appell P., 1925, MEMOR SCI MATH FASC, V3
[8]  
Appell P., 1926, Fonctions hypergeometriques et hyperspheriques, polynomes d'Hermite
[10]  
Askey Richard., 1975, ORTHOGONAL POLYNOMIA